CAT Important Definitions - Practice Questions & MCQ

Chord: A line segment joining two points on a circle is called a chord of the circle. In the figure, AB is a chord of the circle.

Diameter: The chord, which passes through the centre of the circle, is called a diameter of the circle. In the figure, AB is a chord of the circle. A diameter of a given circle is the largest chord of the circle.

The word diameter is used for a chord passing through the centre and also, for its length. If d is the diameter of the circle then d = 2r where r is the radius.

Arc: A piece of a circle between two points is called an arc. 

Let P and Q be two points on the circle. These points P and Q divide the circle into two parts. Each part is an arc. You find that there are two pieces, one longer and the other smaller. The longer one is called the major arc PQ and the shorter one is called the minor arc PQ.

The minor arc PQ is also denoted by  and the major arc PQ by , where R is some point on the arc between P and Q. Unless otherwise stated, arc PQ or stands for minor arc PQ.

If the length of an arc is less than the length of the arc of the semicircle then it is called a minor arc. Otherwise, it is a major arc.

When P and Q are ends of a diameter, then both arcs are equal and each is called a semicircle.

Degree Measure of an Arc

The degree measure of a minor arc is the measure of the central angle subtended by the arc.

Let  be an arc of a circle with centre O. If  then degree measure of . And, we write,.

Segment: The region between a chord and either of its arcs is called a segment of the circular region or simply a segment of the circle.

Again, there are two types of segments, which are the major segment and the minor segment. The segment, containing the minor arc, is called a minor segment and the segment, containing the major arc, is called the major segment. 

Sector: The region between an arc and the two radii, joining the centre to the endpoints of the arc is called a sector. Like segments,  the minor arc corresponds to the minor sector and the major arc corresponds to the major sector.

When two arcs are equal, that is, each is a semicircle, then both segments and both sectors become the same and each is known as a semicircular region.

Concentric Circles: Circles having the same centre but different radius are said to be concentric circles.

Congurent Circles: Two circles C(O, r) and C(O', s) are congruent if they have the same radii i.e. r = s.